This study aims to provide a rigorous theoretical analysis of the natural magnetohydrodynamic (MHD) convection of a viscous, incompressible and electrically conducting fluid within vertical conducting parallel plates. The investigation focuses on the combined influence of thermal radiation, first-order chemical reactions and convective boundary conditions on the flow, heat and mass transfer dynamics.
The governing non-dimensional equations for velocity, induced magnetic field, total induced current, temperature and concentration are derived and solved analytically. The transport equations for temperature and concentration are decoupled and solved in exponential form, while the momentum and magnetic induction equations are treated as a coupled system. Exact solutions are obtained in terms of hyperbolic and exponential functions, incorporating the Biot number to model Newtonian heating/cooling at the channel walls.
The findings reveal that the Hartmann number plays a major role in significantly reducing the energy of motion in the system and it mitigates mass transport and flow friction by generation of the Lorentz force. It is well known that the induced current density depends linearly on the velocity field when the corresponding boundary conditions are given. In addition to this, the extent of heat transfer (Nusselt number) and the mass transfer (Sherwood number) are discovered to be quite responsive to the radiation parameter and the chemical reaction parameter, respectively. In other words, verification with well-known standards reveals a minimal percentage difference, thus the analytical solutions are highly reliable.
This research provides a pioneering analytical framework that simultaneously couples the induced magnetic field with thermal radiation and first-order chemical reactions under generalized convective boundary conditions. A key novelty of this study is the integration of the Biot number to realistically model Newtonian heating and cooling, a factor frequently neglected in idealized isothermal models. The derived closed-form exact solutions provide a high-precision benchmark for the MHD community, revealing a critical competitive relationship: the magnetic damping of the Hartmann number can effectively override the radiative acceleration. These insights offer a transformative strategy for the stability control of high-temperature MHD generators, liquid-metal cooling blankets and advanced nuclear fusion reactors.
